Question

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.

Answer 1

This is a conditional probability problem.

Let A be the event that the person is over 40

Let B be the event that the person is a root beer drinker

Probability of A given B is given by the equation:

$P(A\text{/B)=}\frac{P(AnB)}{P(B)}$$\begin{gathered} P(\text{AnB)}=\frac{AnB}{Total\text{ number of subjects}} \\ P(\text{AnB)}=\frac{30}{255} \\ P(B)=\frac{number\text{ of root b}eer\text{ drinker}}{\text{Total number of subjects}} \\ P(B)=\frac{25+20+30}{255} \\ P(B)=\frac{75}{255} \end{gathered}$

Thus,

$\begin{gathered} P(A\text{/B)=}\frac{30}{255}\div\frac{75}{255} \\ P(A\text{/B)=}\frac{30}{255}\times\frac{255}{75} \\ P(A\text{/B)=}\frac{30}{75} \\ P(A\text{/B)=}\frac{2}{5} \end{gathered}$

Hence , the correct option is option B